Answer at bottom
Step by Step Solution
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STEP
1
:
Equation at the end of step 1
(3•(y2)) ((3-(3•(y2)))+y)
—————————————————+————————————————
(((2•(y2))+5y)-3) (2y-1)•(y+3)
STEP
2
:
Equation at the end of step
2
:
(3•(y2)) ((3-3y2)+y)
—————————————————+————————————
(((2•(y2))+5y)-3) (2y-1)•(y+3)
STEP
3
:
-3y2 + y + 3
Simplify ——————————————————
(2y - 1) • (y + 3)
Trying to factor by splitting the middle term
3.1 Factoring -3y2 + y + 3
The first term is, -3y2 its coefficient is -3 .
The middle term is, +y its coefficient is 1 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant -3 • 3 = -9
Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 1 .
-9 + 1 = -8
-3 + 3 = 0
-1 + 9 = 8
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Equation at the end of step
3
:
(3•(y2)) (-3y2+y+3)
—————————————————+————————————
(((2•(y2))+5y)-3) (2y-1)•(y+3)
STEP
4
:
Equation at the end of step
4
:
(3•(y2)) (-3y2+y+3)
————————————+————————————
((2y2+5y)-3) (2y-1)•(y+3)
STEP
5
:
Equation at the end of step
5
:
3y2 (-3y2 + y + 3)
—————————————— + ——————————————————
(2y2 + 5y - 3) (2y - 1) • (y + 3)
STEP
6
:
3y2
Simplify ————————————
2y2 + 5y - 3
Trying to factor by splitting the middle term
6.1 Factoring 2y2 + 5y - 3
The first term is, 2y2 its coefficient is 2 .
The middle term is, +5y its coefficient is 5 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 5 .
-6 + 1 = -5
-3 + 2 = -1
-2 + 3 = 1
-1 + 6 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 6
2y2 - 1y + 6y - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (2y-1)
Add up the last 2 terms, pulling out common factors :
3 • (2y-1)
Step-5 : Add up the four terms of step 4 :
(y+3) • (2y-1)
Which is the desired factorization
Equation at the end of step
6
:
3y2 (-3y2 + y + 3)
—————————————————— + ——————————————————
(2y - 1) • (y + 3) (2y - 1) • (y + 3)
STEP
7
:
Adding fractions which have a common denominator :
7.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3y2 + (-3y2+y+3) y + 3
———————————————— = ——————————————————
(2y-1) • (y+3) (2y - 1) • (y + 3)
Canceling Out :
7.2 Cancel out (y + 3) which appears on both sides of the fraction line.
Final result :
1
——————
2y - 1
Step-by-step explanation: